Project Summary Left truncation arises frequently in observational cohort studies, in which subjects are sampled into substudies at some time during their follow-up, but the time origin of interest occurred prior to substudy sampling. For example, in the National Alzheimer's Coordinating Center (NACC) cumulative data set, many subjects experienced onset of cognitive impairment prior to their entry to the data set, and thus their time from impairment to Alzheimer's disease (AD) diagnosis is left truncated by their time to NACC entry. Standard methods of risk set adjustment can be used to adjust for this delayed entry, as long as the critical assumption of quasi-independence (i.e., factorization of the joint density over the observable region) between the entry time and time to AD diagnosis holds. However, this assumption often does not hold, and the simple adjusted analyses are biased. Truncated data, unlike purely censored data, enable identification of this requisite dependence due to joint observation of both the entry (truncation) time and the event time, and formal statistical tests are available. This proposal is motivated by our team's collective and extensive engagement in neurological disease studies, which display pervasive dependent truncation, and is supported by our expertise in survival analysis. This proposal adopts a range of analytical approaches to address dependent truncation that arises through any of several possible mechanisms. We accommodate unexplained dependence through inversion of transformation models and permutation null distributions, nonparametric bounds and estimation, and semi-parametric models, covariate-induced dependence through inverse probability weighting methods, and dependence that is induced by sequential truncating events through copula models. This project will establish a significantly enhanced collection of usable and robust methods for the analysis of dependently truncated data, which will strengthen the validity of research findings from studies of major public health problems, such as Alzheimer's disease. Each of our aims involves derivation of asymptotic results, extensive simulation, and application to our motivating neurologic disease studies.